Mode coupling bi-stability and spectral broadening in buckled carbon nanotube mechanical resonators

Abstract

Bi-stable mechanical resonators play a significant role in various applications, such as sensors, memory elements, quantum computing and mechanical parametric amplification. While carbon nanotube based resonators have been widely investigated as promising NEMS devices, a bi-stable carbon nanotube resonator has never been demonstrated. Here, we report a class of carbon nanotube resonators in which the nanotube is buckled upward. We show that a small upward buckling yields record electrical frequency tunability, whereas larger buckling can achieve Euler-Bernoulli bi-stability, the smallest mechanical resonator with two stable configurations to date. We believe that these recently-discovered carbon nanotube devices will open new avenues for realizing nano-sensors, mechanical memory elements and mechanical parametric amplifiers. Furthermore, we present a three-dimensional theoretical analysis revealing significant nonlinear coupling between the in-plane and out-of-plane static and dynamic modes of motion, and a unique three-dimensional Euler-Bernoulli snap-through transition. We utilize this coupling to provide a conclusive explanation for the low quality factor in carbon nanotube resonators at room temperature, key in understanding dissipation mechanisms at the nano scale.

Nanomechanical Resonators: Toward Atomic Scale

“…In MEMS structures, the shape of a beam made from metal or dielectric is usually defined in a top-down lithographic patterning process, and its static profile cannot be easily modified in a continuous and substantial way by electrostatic forces. In contrast, the amount of slack and mechanical tension in a nanotube is difficult to control in the fabrication process and can vary strongly between nominally identical devices. , Nevertheless, a gate electrode in the microtrench under the nanotube offers a convenient tool to control the resonator tension via the electrostatic force. ,,,− , This force changes the nanotube shape significantly and thus induces tensile strain in nanotube, which enables frequency tuning ,,− ,− (Section ) and mode coupling (Section ). In addition, a static force applied on a straight nanotube breaks the symmetry of a harmonic potential due to bending of the nanotube, which leads to a striking behavior where the equilibrium position of the mode can be controlled by its vibration amplitude, as illustrated in Figure .…”

“…In contrast, the amount of slack and mechanical tension in a nanotube is difficult to control in the fabrication process and can vary strongly between nominally identical devices. 97 , 109 Nevertheless, a gate electrode in the microtrench under the nanotube offers a convenient tool to control the resonator tension via the electrostatic force. 11 , 110 , 94 , 96 − 98 , 111 This force changes the nanotube shape significantly and thus induces tensile strain in nanotube, which enables frequency tuning 11 , 94 , 96 − 98 , 109 − 112 ( Section 7.1 ) and mode coupling ( Section 10.1 ).…”

“… 97 , 109 Nevertheless, a gate electrode in the microtrench under the nanotube offers a convenient tool to control the resonator tension via the electrostatic force. 11 , 110 , 94 , 96 − 98 , 111 This force changes the nanotube shape significantly and thus induces tensile strain in nanotube, which enables frequency tuning 11 , 94 , 96 − 98 , 109 − 112 ( Section 7.1 ) and mode coupling ( Section 10.1 ). In addition, a static force applied on a straight nanotube breaks the symmetry of a harmonic potential due to bending of the nanotube, which leads to a striking behavior where the equilibrium position of the mode can be controlled by its vibration amplitude, 97 as illustrated in Figure 4.2 .…”

Micromachined Mechanical Resonant Sensors: From Materials, Structural Designs to Applications

“…[ 112 ] The design of bulked CNTs can yield lower resonant frequencies while offering bi‐stability and spectral broadening for sensing and other applications. [ 22 ] Conventional circularly clamped membranes, on the other hand, possess the advantage of high resonant frequencies. [ 122 ] This configuration is commonly utilized in 2D materials with naturally occurring nanoflake structures, enabling easy actuation using electrostatic forces, [ 120 ] Figure 9D.…”

“…The MMRs are the core component of resonant sensors that have found useful applications, ranging from probing material properties, a better understanding fundamental science and physics to device applications. [19][20][21][22][23] In respect to their practical applications, MMRs and resonant sensors are usually found in timing references, atomic force microscopy (AFMs), accelerometers and mass sensing devices. [24] In the areas of chemical and biological applications, micromachined resonators are for use in monitoring small molecules, and this aspect has attracted massive attention over the past decades especially in healthcare, food and environmental safety, and biosecurity.…”